A stationary irregular seastate can be represented by a wave vari- ance spectrum, S ( ω). A finite wave elevation time series can be rep- resented as the sum of a large number of harmonic wave compo- nents with uniformly distributed random phase angles. The number of harmonic components is the number of frequency intervals used to discretize the wave spectrum. Besides the randomly chosen phase angles, it has been shown by Tucker [ 17 ] that also the wave am- plitudes must be chosen randomly so that wave group statistics are realistically reproduced. Since the low frequency wave drift forces are closely connected to the wave group envelope, it is important to con- sider the wave amplitude randomness for the numerical simulations. Following [ 17 ], the free surface elevation is given by: