A note on the statistics of threshold crossing for a nonlinear wave field

Based on the non-Gaussian joint elevation and slope density function developed by Huang et al. (1984), the expected number of threshold crossing at an arbitrary level for a nonlinear wave field is derived. The distribution of the expected threshold crossing per unit time as a function of the crossing level is skewed with respect to the mean water level. This skewness also causes the mean zero crossing per unit time to deviate from the expected frequency of the wave field.