ARMA Algorithms for Ocean Wave Modeling

Three different algorithms are presented for simulating a time series which is compatible with a given power spectrum of ocean waves. The first algorithm generates the current value of the time series as the sum of a linear combination of its past values and a white noise deviate. The second algorithm produces the values of the time series as a linear combination of white noise deviates. The third algorithm is a combination of the first and second algorithms. These algorithms are applied to the Pierson-Moskowitz (P-M) spectrum, exclusively. The third algorithm is associated with simple analog filter approximations of the P-M spectrum. The advantages and disadvantages of each of the three algorithms are discussed in context with their applicability to offshore engineerng problems.