  By means of the direct numerical simulation of directional waves on the
surface of deep water it is shown that extreme waves can exhibit such asymmetry
that the occurrence of deeper troughs is several times more likely on the wave
rear slopes. This effect becomes most pronounced in the case of steep
short-crested waves. It is not related to the Benjamin - Feir instability, but
is a result of complex contribution from nonlinear combination harmonics,
mainly cubic in nonlinearity. The discovered asymmetry can lead to remarkably
different estimates of the rogue wave probability based on either down- or
up-zero-crossing methods for individual wave selection, commonly used in the
oceanography.
