## Forecasting extreme waves

*Numerical reconstruction of the random 3D sea surface*

We developed a stochastic model for probabilistic forecasting of extreme waves. The coupled standard spectral wave models for marine forecasting with a phase resolving model, which solve the primitive wave equation using a Higher Order Spectral Method (HOSM). Basically the HOSM receives as input the wave spectra from the standard forecasting model, reconstructs initial Gaussian random sea surfaces with different random amplitude and phases and computes Monte Carlo simulations of the temporal evolution of the initial surfaces. Results are post processed to provide wave statistics and probability of extreme for the given sea states.

An application of this method is published in Bitner-Gregersen E.M., Fernandez L., Lefèvre, J.M., Monbaliu, J., **Toffoli, A.**, 2014. The North Sea Andrea storm and numerical simulations. *Nat. Hazards Earth Syst. Sci.*, 14, 1407–1415. doi:10.5194/nhess-14-1407-2014 , where a coupling of a spectral wave model with a non- linear phase-resolving model is used to reconstruct the evolution of wave statistics during a storm crossing the North Sea on 8–9 November 2007. During this storm a rogue wave (named the Andrea wave) was recorded at the Ekofisk field. The wave has characteristics comparable to the well-known New Year wave measured by Statoil at the Draupner plat- form 1 January 1995. Hindcast data of the storm at the near- est grid point to the Ekofisk field are here applied as input to calculate the evolution of random realizations of the sea surface and its statistical properties. Numerical simulations are carried out using the Euler equations with a higher-order spectral method (HOSM). Results are compared with some characteristics of the Andrea wave record measured by the down-looking lasers at Ekofisk.