Slope distribution in front-back asymmetric stochastic Lagrange time waves

The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. This paper presents the slope distributions and other characteristic distributions at level crossings
for asymmetric Lagrange time waves, i.e. what can be observed at a fixed measuring station, thereby extending results previously given for space waves. The distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are: slope in time, slope in space, and vertical particle velocity when the waves are observed close to instances when the water level crosses a predetermined level.
The theory has been made possible by recent generalizations of
Rice's formula for the expected number of marked crossings in random
fields.