Shallow-water version of the Freak Wave Warning System

The ECMWF freak wave warning system is based on a random time series analysis using the envelope wave height. The key quantity of interest is the maximum envelope wave height distribution which for (weakly) nonlinear systems depends on envelope skewness and kurtosis. Expressions for skewness and kurtosis for general spectra are presented, but they are very cumbersome. Therefore, a simple parametrization of skewness and kurtosis of the bound waves and the contribution of the free waves to kurtosis is presented. These parametrisations are validated against computations using the theoretical expressions of the statistical parameters. By adjusting some free parameters in the parametrizations a good agreement with the ’exact’ computations is found. It is suggested to use these parametrizations in the operational version of ECMWF’s freak wave warning system.