  The conditional value of a stationary random process, given the
level-upcrossing of another dependent stationary random process, is considered.
Assuming that both processes are weakly non-Gaussian, an analytical
approximation for the related conditional distribution is derived. It is based
on a trivariate Edgeworth expansion truncated to non-Gaussian terms of lowest
order, to which Rice's formula is then applied. As an application, the effect
of level-upcrossing conditioning in second-order ocean waves is investigated.
Upcrossing events are monitored for the sea surface elevation. The conditional
distributions of different kinematic variables, given upcrossing, are
considered for different sea-state configurations. Predictions from the
analytical model are compared with numerical data obtained from Monte Carlo
experiments. It is found that the analytical approximation provides conditional
mean and variance in good agreement with numerical data, although moderate
discrepancies appear for the sea states with the most severe wave cambers.
Regarding the conditional skewness, given upcrossing, results are mixed, with
significant discrepancies between the analytical approximation and numerical
estimates, in a number of cases. An Edgeworth-type approximation is also
provided for the upcrossing frequency and compared with Monte Carlo estimates;
this analytical estimate is found to be accurate over a wide range of crossing
levels.
