Power-law Scaling and Probabilistic Forecasting of Tsunami Runup Heights

Abstract

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.

Probabilistic Analysis of Tsunami Hazards*

“…It has been shown in previous studies (Soloviev, 1969;Houston et al, 1977;Horikawa and Shuto, 1983;Burroughs and Tebbens, 2005) that at a given coastal location, tsunami amplitudes follow a definable frequency-size distribution over a sufficiently long amount of time. For regions with an extensive catalog of observed tsunami wave heights, this method can be of great use in establishing tsunami probabilities.…”

“…More recently, Burroughs and Tebbens (2005) proposed that tsunami runup heights follow a power-law relationship similar to many other natural systems, particularly the Gutenberg-Richter frequency-magnitude relationship for earthquakes. In examining extensive records of tsunami wave heights at several locations in Japan, they conclude that the cumulative frequency-size distribution is best fit by a power-law relationship of the form…”

“…Recent research has also shown that many other physical phenomena follow a power-law frequency-size distribution (e.g., Ito and Matsuzaki, 1990;Birkeland and Landry, 2002;Malamud et al, 2004). In addition to the form of the scaling relationship used (i.e., exponential, power-law), Burroughs and Tebbens (2005) provide two criteria to determine whether a particular frequency-size distribution can be used for probabilistic forecasting: (1) the scaling exponent (a) should be the same for both short and long time intervals and (2) the scaling relationship from the data excluding the largest events in the catalog should be consistent with those largest events. For cases where a best-fit upper-truncated power law is caused by an incomplete catalog missing large events, Burroughs and Tebbens (2005) indicate that a power-law relationship should be used for probabilistic assessments.…”

“…Errors associated with this type of measurement are discussed by Baptista et al (1993) and Borrero (2001) and are usually in the 1-m range. For tide gauge data, minimum tsunami amplitudes reported in catalogs are approximately 0.1 m (Burroughs and Tebbens, 2005), owing primarily to ambient wave activity in harbors. With maximum tsunami amplitudes in the 30-40 m range, conventional measurements span less than three orders of magnitude in amplitude.…”

Simulation-Based Probabilistic Tsunami Hazard Analysis: Empirical and Robust Hazard Predictions

“…In the first category, PTHA is conducted using tsunami catalogs (Burroughs and Tebbens 2005;Kulikov et al 2005;Tinti et al 2005;Orfanogiannaki and Papadopoulos 2007), whereas in the second category, different ''scenario-based'' PTHA methods are suggested (Geist and Dmowska 1999;Downes and Stirling 2001;Farreras et al 2007;Liu et al 2007;Power et al 2007;Yanagisawa et al 2007; Burbidge et al 2008;González et al 2009;Løvholt et al 2012). In the third category, a combination of the previous two is considered (Geist 2005;Geist and Parsons 2006;Annaka et al 2007;Thio et al 2007;Burbidge et al 2008;Parsons and Geist 2009;Grezio et al 2010Grezio et al , 2012Horspool et al 2014;Fukutani et al 2016).…”