For the design of offshore structures it is important to accurately predict wave runup and thus avoid topside inundation and minimize the wave impact on the underside of the deck structure. In this paper a three-parameter probability distribution function for nonlinear wave run-up amplitudes is presented. It builds upon previous studies and utilizes the quadratic transformation of incident waves. The parameters of this probability distribution are estimated from the data using method of L-moments and the explicit relation between the parameters and L-moments is presented. The L-moments themselves are linear combinations of ordered data and consequently they are less influenced by outliers and unexpectedly large values. Earlier theoretical models, based on simplified diffraction theory, are presented and compared with the L-moments model. A three-parameter Weibull distribution model that utilizes the method of L-moments is derived and discussed. Run-up measurements from a mini-TLP model test program are used as the basis for comparison of the three methods. This study demonstrates that the new empirical model and Weibull distribution are more robust in representing the probability distribution of nonlinear runup amplitudes especially for the weakly nonlinear cases with moderate steepness. Although the new empirical model and Weibull distribution have different probability structure their estimates are found to be fairly close.

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