A highly efficient numerical procedure for the computer based prediction of nonlinear deep water ocean surface waves is presented. To reconstruct consistent initial conditions from measured surface elevation data, the approach employs a combination of a high order spectral method with Krylov subspace techniques. Aiming at prediction horizons of a few minutes, the method allows real-time prediction of sea states for domains of several square kilometres. Taking the nonlinearity of the wave evolution equations into account leads to a substantial increase in accuracy of the prediction at only moderate additional cost.
