Effects of Tides on Maximum Tsunami Wave Heights: Probability Distributions

Abstract

A theoretical study was carried out to understand how the probability distribution for maximum wave heights (?m) during tsunamis depends on the initial tsunami amplitude (A) and the tides. It was assumed that the total wave height is the linear sum of the tides and tsunami time series in which the latter is decaying exponentially in amplitude with an e-folding time of 2.0 days, based on the behavior of observed Pacific-wide tsunamis. Direct computations were made to determine the statistics of maximum height for a suite of different arrival times and initial tsunami amplitudes. Using predicted tides for 1992 when the lunar nodal f factors were near unity during the present National Tidal Datum Epoch 1983?2001, the results show that when A is small compared with the tidal range the probability density function (PDF) of the difference ?m ? A is closely confined in height near mean higher high water (MHHW). The ?m ? A PDF spreads in height and its mean height ?o ? A decreases, approaching the PDF of the tides and MSL, respectively, when A becomes large compared with the tidal range. A Gaussian form is found to be a close approximation to the ?m ? A PDF over much of the amplitude range; associated parameters for 30 coastal stations along the U.S. West Coast, Alaska, and Hawaii are given in the paper. The formula should prove useful in probabilistic mapping of coastal tsunami flooding.