Tsunami runup on steep slopes: How good linear theory really is

This is a study of the application of linear theory for the estimation of the maximum runup height of long waves on plane beaches. The linear theory is reviewed and a method is presented for calculating the maximum runup. This method involves the calculation of the maximum value of an integral, now known as the runup integral. Laboratory and numerical results are presented to support this method. The implications of the theory are used to reevaluate many existing empirical runup correlations. It is shown that linear theory predicts the maximum runup satisfactorily. This study demonstrates that it is now possible to match complex offshore wave-evolution algorithms with linear theory runup solutions for the purpose of obtaining realistic tsunami inundation estimates.