Simulation of stochastic ocean states by random function methods

In the two classical simulation methods for stationary stochastic processes, namely the spectral representation methodology and the orthogonal expansion method, the standard orthogonal random variables were defined as orthogonal function forms of a given basic random variable, so that the original stochastic process was then represented by one basic random variable. In order to analyse a stochastic process from a set of sample functions, discrete representative points of the basic random variable were selected, and sample functions with assigned probability were generated directly by the spectral representation methodology and the orthogonal expansion method, respectively. The two innovated methods were used to simulate random ocean states, and the simulated results are in excellent agreement with the prescribed probabilistic characteristics. Some features of these two kinds of innovated simulation methods in applications were described and compared.