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The conditional value of a stationary random process, given thelevel-upcrossing of another dependent stationary random process, is considered.Assuming that both processes are weakly non-Gaussian, an analyticalapproximation for the related conditional distribution is derived. It is basedon a trivariate Edgeworth expansion truncated to non-Gaussian terms of lowestorder, to which Rice's formula is then applied. As an application, the effectof level-upcrossing conditioning in second-order ocean waves is investigated.Upcrossing events are monitored for the sea surface elevation. The conditionaldistributions of different kinematic variables, given upcrossing, areconsidered for different sea-state configurations. Predictions from theanalytical model are compared with numerical data obtained from Monte Carloexperiments. It is found that the analytical approximation provides conditionalmean and variance in good agreement with numerical data, although moderatediscrepancies appear for the sea states with the most severe wave cambers.Regarding the conditional skewness, given upcrossing, results are mixed, withsignificant discrepancies between the analytical approximation and numericalestimates, in a number of cases. An Edgeworth-type approximation is alsoprovided for the upcrossing frequency and compared with Monte Carlo estimates;this analytical estimate is found to be accurate over a wide range of crossinglevels.

Level-crossing distributions of kinematic variables in multidirectional second-order ocean waves