This paper examines the probability density function (PDF) of free water surface elevations in coastal areas. The functional form and properties of PDFs of extreme storms propagating over a mildly sloping bathymetry are investigated. This is facilitated through comparisons between experimental measurements and a wide range of probability models; the latter including both analytical and
empirical distributions. The incident wave conditions correspond to realistic storm spectra (JONSWAP) and have been simulated as long random timeseries of 60-hour duration. The length of the records is sufficient to provide an accurate description of distribution tails. Six sea-states with
varying offshore steepness have been generated and measured at different cross-shore locations. The
cross-shore evolution of the wavefield initially leads to the development of nonlinear harmonics, both at low and high frequencies, and a broadening of the wave spectrum. This is enhanced by wave breaking particularly at shallower water depths or steeper sea-states. These result in rapid deviations from Gaussian theory with respect to the PDFs of surface elevations. Available models are generally
successful in capturing nonlinear evolution arising at a second-order of wave steepness but cannot model the probability structure once a significant proportion of waves are breaking. In comparing the deviations between experimental data and model predictions, the best performing model is identified.