Forecasting the heights of later waves in Pacific-wide tsunamis

A method is derived to forecast the extreme heights of later waves in Pacific-wide tsunamis, for locations in the vicinity of real-time reporting tide gages. The forecast for wave peaks has the form eta(F)(t) = eta(B)(t) + eta(e)(t), where eta(e) = A sigma exp[-(t - t(o))/tau]. Here, the forecast begins at time t = t(o), which is 4 h after tsunami detection at a tide gage, sigma is the standard deviation of tsunami-band fluctuations observed in the 2-h time interval before the forecast begins, eta(B) is a background water level prediction that includes the tides and lower frequency oscillations, tau = 48 h is an e-folding decay constant, and A = 3.0 is a constant coefficient. Placing a minus sign in front of eta(e) provides a forecast for wave troughs. This form for the forecast, and the values of the parameters, are justified using probability theory and Monte Carlo simulations based on 3000 synthetic tsunami time series. The method is then tested successfully (i.e., agreement within 0.5 m) against six past Pacific-wide tsunamis, as observed at U.S. tide gages. These case studies include the five major tsunamis to produce loss of life and/or substantial damage to U.S. coastal communities during the Twentieth Century. The sixth study is the 1994 Shikotan tsunami, which is the latest Pacific-wide tsunami to trigger tsunami warnings for U.S. regions. Algorithms for detecting local tsunami onset and generating forecasts are given in an appendix, together with a description of the wavelet method used to generate the synthetic tsunami series.