| Abstract: | Three practical methods for computing the expected maxima of Gaussian time series for ocean system analysis are developed. These methods utilize Pierce's sample scaling concept to overcome the maxima counting and correlation difficulties, but minimize the associated complexity and uncertainties. The first (Direct) method removes the dependence on the envelope for maxima estimation of the time series by directly operating on the time series itself. The second (Poisson clumping) employs the notion of sample scaling factor, but requires neither computing the envelope nor segmenting. The third (Log-fit) is a simple logarithm curve fitting, using the slowly varying, logarithmic growth property of the expected maximum. The accuracy and computational efficiency of these methods are examined. The Direct method and the Poisson clumping method are found to have comparable accuracy. Employment of the envelope does not improve the accuracy of the estimate in practice. Hence, the Direct method and the Poisson clumping method should be preferred. The Poisson clumping method is more efficient than both the Direct method and Pierce's method because of its straightforwardness in implementation. The Log-fit method is the simplest to implement, and computationally the most efficient. Its accuracy is acceptable for many engineering preliminary designs. |
