  A major challenge in next-generation industrial applications is to improve
numerical analysis by quantifying uncertainties in predictions. In this work we
present a formulation of a fully nonlinear and dispersive potential flow water
wave model with random inputs for the probabilistic description of the
evolution of waves. The model is analyzed using random sampling techniques and
non-intrusive methods based on generalized Polynomial Chaos (PC). These methods
allow to accurately and efficiently estimate the probability distribution of
the solution and require only the computation of the solution in different
points in the parameter space, allowing for the reuse of existing simulation
software. The choice of the applied methods is driven by the number of
uncertain input parameters and by the fact that finding the solution of the
considered model is computationally intensive. We revisit experimental
benchmarks often used for validation of deterministic water wave models. Based
on numerical experiments and assumed uncertainties in boundary data, our
analysis reveals that some of the known discrepancies from deterministic
simulation in comparison with experimental measurements could be partially
explained by the variability in the model input. We finally present a synthetic
experiment studying the variance based sensitivity of the wave load on an
off-shore structure to a number of input uncertainties. In the numerical
examples presented the PC methods have exhibited fast convergence, suggesting
that the problem is amenable to being analyzed with such methods.
