Forecasting the Heights of Later Waves in Pacific-Wide Tsunamis

Abstract

A method is derived to forecast theextreme heights of later waves in Pacific-widetsunamis, for locations in the vicinity of real-timereporting tide gages. The forecast for wave peaks hasthe form η_F(t) = η_B(t) + η_e(t),where η_e = Aσ exp [- (t - t_o)/τ ]. Here, the forecast begins attime t = t_o, which is 4 h after tsunamidetection at a tide gage, σ is the standarddeviation of tsunami-band fluctuations observed in the2-h time interval before the forecast begins,η_B is a background water level predictionthat includes the tides and lower frequencyoscillations, τ = 48 h is an e-folding decayconstant, and A = 3.0 is a constant coefficient.Placing a minus sign in front of η_e providesa forecast for wave troughs. This form for theforecast, and the values of the parameters, arejustified using probability theory and Monte Carlosimulations based on 3000 synthetic tsunami timeseries. The method is then tested successfully (i.e.,agreement within 0.5 m) against six past Pacific-widetsunamis, as observed at U.S. tide gages. These casestudies include the five major tsunamis to produceloss of life and/or substantial damage to U.S. coastalcommunities during the Twentieth Century. The sixthstudy is the 1994 Shikotan tsunami, which is thelatest Pacific-wide tsunami to trigger tsunamiwarnings for U.S. regions. Algorithms for detectinglocal tsunami onset and generating forecasts are givenin an appendix, together with a description of thewavelet method used to generate the synthetic tsunamiseries.