Power Scaling to Forecast Water Height and Life Loss in Japan Tsunamis

Abstract

We introduce power functions to forecast the probability of occurrence and recurrence intervals of tsunamis the size of the great 3/11/2011 Tohoku event in Japan. Two measures of tsunami magnitude are used; tide gauge water height and life loss, for five specific locations in Japan, and maximum water height (by any measure) and life loss for all of Japan. For all measures, data are well fit by power scaling functions on size-cumulative frequency plots, which are the basis of probabilistic forecasts. The historic Japanese tsunami data, including the 3/11/2011 tsunami, are from the NOAA National Geophysical Data Center. The data were aggregated for all of Japan, and for five specific locations on the east coast of Honshu Island, the area most affected by the 3/11/2011 event. Tide gauge water heights at the five locations are well fit by power functions with scaling exponents ranging between 0.9 and 1.6 for water heights ranging between 1.21 and 4.0 meters. The recurrence interval for a tide gauge tsunami water height reported for the 3/11/2011 tsunami at each location, ranges from 70 to 487 years. Maximum water heights (measured by any method) for all of Japan from 684 to 2003 exhibit power scaling with a scaling exponent of 0.7. The recurrence interval for a maximum tsunami water height of 40 m (reported for the 3/11/2011 tsunami) or greater, at any location along the Japanese coast, is ~264 years. Tsunami life loss for specific locations in Japan from 1905 to 1993 exhibits power scaling with a scaling exponent of 0.72. The recurrence interval for the maximum life loss experienced at any location in Japan due to a tsunami of the size reported for the 3/11/2011 event is ~132 years.